Electrical analogues



June 10, 1958 A. D. GARRISON ELECTRICAL ANALOGUES Original Filed June13. 1949 FIG.

F/XED ELECTRODE32) PAR T/ T/ ON 22 HORIZONTAL TANK l2 RCORD/NG POTENT/0M5 TER PART/ T/ON 2 3 0 3 M m w m H m M m 0 0 L P w E M 0 w MPARTITION 22 WELL AXIS/0 3 2 m T in 2 .P G H I 2 m m 0 L B w m M m T /\vw K N m TL/QU/D L EVEL l8 I TANK BOTTOM ll INVENTOR. ALLEN 0. GARR/SON'BY g AT TORNE Y ELECTRICAL AN ALOGUES Allen D. Garrison, La Jolla,Calif., assignor to Texaco Development Corporation, New York, N. Y., acorporation of Delaware Continuation of application Serial No. 98,666,June 13, 1949. This application April 5, 1956, Serial No. 576,428

7 Claims. Cl. 235-61) This invention relates to potentiometric modelsemployed for the solution of problems encountered in the investigationof electrical, magnetic, mechanical, hydraulic, and thermal systems, andis concerned particularly with establishing and maintaining requiredpotential differences across conductive barriers employed to separateadjacent pools of electrolyte in such models. The invention providesmethods and apparatus to this end.

This application is a continuation of my copending application SerialNo. 98,666, now abandoned, which was filed on June 13, 1949.

As disclosed in Patent No. 2,569,816 which issued on October 2, 1951, inthe name of Burton D. Lee, Patent No. 2,569,510 which issued on October2, 1951, in the name of Alexander Wolf, and Patent No. 2,547,950 whichissued on April 10, 1951, to Herzog and Lee, a number of mechanical,magnetic, electrical and thermal systems obey Laplaces equation, atleast approximately. By way of example, there is a complete analogybetween the flow of an uncompressed fluid in a porous medium and theflow of electricity in a conductor. This analogy has been applied to thesolution of oil and gas field problems through the construction ofelectrical analogues. These employ a conductive model, say a pool ofelectrolyte the shape of which is analogous to that of the petroleumproducing structure undergoing investigation. If the structure iscomposed of rocks of different permeability and the boundaries betweenthese rocks is known, a conductive barrier may be introduced into themodel to simulate the boundary, and the difference in permeabilitysimulated by employing pools of electrolyte having diiferentresistivities corresponding respectively to the permeabilities of therocks represented. Wells in the structure are represented by electrodesprojecting into I the pool. In the case of a gas condensate field beingsubjected to a cycling operation, some of the electrodes may representinjection wells and others extraction wells. Exploration of thepotential gradients set up in the pool by the electrodes permitsaccurate mapping of the in vasion front of the dry gas being pumped intothe injection wells to displace wet gas removed through the extractionwells.

Similar analogies may be drawn between the flow of electricity in a poolof electrolyte and the conduction of heat in solid thermal conductors,the distribution of mechanical stresses in a loaded structure, thedistribution of flux in electrical, magnetic and electromagnetic fieldsand the distribution of potentials in a well bore and its surroundingformations in the earth. So the potentiometric model or analoguetechnique is applicable to problems arising in all of the foregoingcases, examples being the design of hydraulic structures such as dams,the design of electrical apparatus including condensers, insulators,conductive terminals and electrical discharge devices such as vacuumtubes, radiation counters, electrostatic lenses, etc., and theinvestigation of the fundamentals of electrical logging of oil wells andthe like.

States Patent 0 Electrical logging is much employed in oil and gasfields to investigate the nature and thickness of the various earthformations penetrated by wells. In electrical logging, currents are setup in the mud or liquid in the well-bore and in the formations and theeitects of these currents are measured with one or more exploringelectrodes which are drawn through the bore, observed potentials beingplotted against well depth. In this fashion both self potential andresistivity logs are obtained and yield valuable information withrespect to subsurface geology. The interpretation of self potential andresistivity logs obtained in such wells depends upon a number oftheoretical considerations which cannot be verified in logging of actualwells because of the large number of unknowns and the complexitiesinvolved due to the fact that ordinarily a well penetrates a largenumber of beds or formations. An electrical analogue employing apotentiometric model of a well and its surrounding formations lzas beendeveloped by Herzog and Lee and is disclosed in the aforementionedPatent No. 2,547,950. By means of this analogue various theories andhypotheses employed in Well log interpretation may be subjected tocheck.

The technique developed by Herzog and Lee employs a potentiometric modelwith the axis of the well bore lying horizontally. The well bore isrepresented by a long narrow compartment, and the beds penetrated by thewells are represented by a series of compartments adjoining the side ofthe well bore compartment. The side of the well bore compartment and thepartitions between the compartments representing the beds are imperviousupright Walls or barriers. Each compartment contains a pool ofelectrolyte (say a Water solution of a salt) having a resistivitycorresponding to that of the body which it represents. Thus the pool inthe well bore compartment has its resistivity adjusted to correspond tothe resistivity of the mud in the actual bore hole represented, and thepools in the respective bed compartments have their resistivitiesadjusted to correspond to the beds represented.

The walls or partitions which separate the bed compartments from eachother and the well bore compartment must be impervious to theelectrolyte, and means must be provided for transmitting current acrosseach partition substantially throughout its length but incapable oftransmitting current lengthwise of the parti tion. One way ofaccomplishing this result is to hand a series of fine wire Us over apartition of insulating material, the Us being spaced close together butnot touching. Each U dips into the pools of electrolyte on oppositesides of the partition and is capable of transmitting current from onepool to the other across the partition, but there is no conductionlengthwise across the partition. Another way of accomplishing thisresult is to employ a partition of nonconductive plastic material havinga grid of conductive wires embedded in it, each wire running directlyacross the partition and in,- sulated from the other wires. In short,the partition is a conductor in one direction in space only, i.e.,normal to its own surface.

A resistivity log is obtained by energizing the model just describedwith electric current, just as in resistivity logging of an actual well,and exploring the well bore.

compartment by passing one or more measuring elec-' trodes along it, tosimulate the exploration in an actual well bore.

In making a self potential log of a well, a movable electrode connectedto the end of an insulated cable is passed along the well bore, which isfilled with drilling mud. The upper end of the cable is connected to arecording potentiometer.

The other terminal of the po- 'tentiometer is connected to a secondelectrode grounded at a fixed point on the surface, and the potential atthis point. is arbitrarily assumed to be. zero. Therefore,r for eachposition of the movable. electrode in the bore, the potentiometerrecords the relative potential. These relative. potentials are plottedagainst Well depth, usually by direct recording and. the result is theself potential log;

The self potential" log of a well isaftected by various factors, not allof which are as yet clearly understood. However, it is generallyaccepted that the self potential" is caused by voltage diiferences whichexist at the boundaries or interfaces between adjoining beds and betweenthe. beds and the fluid in the well. These voltages in turn depend onthematerials which compose the beds and. onthe fluids contained in theWelland in the beds, as well as upon pressure differences between thefluid in the well and those in the beds. For practical purposes, theaforementioned factors may be grouped into a series of potentialdifferences distributed along the boundaries (:2) between beds and (b)between the beds and the well.

These differences can be represented in the well model described byemploying barriers which set up potential difierences between adjacentpools, although in addition the resistivities of the several pools haveto be adjusted as explained previously. One way to set up the requiredpotential diii'erence across the barrier is described by Lee and Herzogin their aforementioned application. They employ arr-insulatingpartition having a great number of wires passing through it, as alreadydescribed, but u the several wires are built of two differentconductors. Thus each wire may have a right half ofiron-Welded to a lefthalf of copper so that a contact voltage is produced at the junction,the junctions being embedded in the insulator out of which the barrieris built. the barrier is a wall with a large number of built-inbatteries or galvanic piles. By selecting different metal couples,different voltage differences can be set up through the barrier.

The instant invention is directed to a different way of setting up therequired potential difference across a barrier in a potentiometric modelbetween two pools of electrolyte. Thus the invention contemplatesdeveloping a fixed but adjustable potential across a barrier separatingtwo pools of electrolyte in a potential model by disposing a solidelectrical conductor across the barrier and carrying on anelectrochemical oxidation=reduction reaction (as in anoxidation=reduction cell) in one of the poolsand controlling the actionby controlling ion activity in the pool.

If desired, the metal of the conductor'can be the same as that of theions in the pool, an example being two pools of aqueous copper sulphatesolution separated physically by a barrier but connected electrically bya copper conductor as in a concentration cell.

The potential of the end of a copper wire relative to that of acopper-containing electrolyte is a function of the activity of thecopper ions (Cu) in the electrolyte. If the activity of the Cu-ions isincreased by adding more copper salt to the solution, the copper wire incontact with the solution becomes more positive. The change in thevoltage of the wire, when the activity is changed from A to A can becalculated by the Nernst equation:

wherein, R is the molar gas constant in Joules; T the kelvintemperature; n the valence of the ion in question; F the Faraday incoulombs.

For a temperature of 25 C., and using copper which has. )1 equal 2, theequation becomes:

Vo1ts=.0296 log Ag/A Thus, if the activity of the copper ionsin anelectrolyte pool on the right hand side of abarrier composed. of

Change in voltage= gj in In effect, s

insulating material with a number of copper wires run ning throughit is,say, .01 mol/liter, and the activityof the ions in another electrolytepool on the left is .00} mol/liter, then the electrolyte in the righthand pool will be .0296 volts more negative than the electrolyteimmediately across the barrier. in.the left hand pool. With uniformelectrolyte activity this same potential difierence will exist betweenopposite sides of the barrier over its entire extent.

The above-described potential difi'crence can be controlled byadjustments in the difference in copper ion activity. If it is desiredto make the potential difference very large, this may be accomplished byputting a material (say ammonia) into one of the-electrolytes whichdraws the copper ion into a weakly ionized complex.

independent control. over boththe potential across the barrier and theelectrical conductivity on either side can be obtained by adding anionizable salt to the electrolyte where it is desirable to increase theconductivity, making the choice of salt such that its ions are inert tothe copper electrode and do not alter the copper ion activity. Forexample, if the copper ion activity has been adjusted by adding coppersulfate to the water, and it is necessary to make the solution a betterconductor, potassium chloride may be used for the purpose. The voltageof the end of the copper wire which contacts this solution will dependon the activity of the copper ions only, and, within reasonable limits,will not-be influenced by the potassium and chloride ions.

The wires in the partition may consist of some metal other than copper,such as zinc, or cadmium, and the electrolytes'may be adjusted byvarying the activity of Zinc ions or cadmium ions respectively.

Two barriers'or partitions such as those described can be used tocontact the same solution and yet be made independently variable. Onepartition may be traversed by copper wires, and'the other by silverwires. In such' case, the solution contains, for example, copper sulfateto determine the copper wire potential and potassium" chloride todetermine the silver potential, since silver chloride will precipitateon the ends of thesilver wires. The overall conductivity can be alteredby sodium nitrate;

The sodium nitrate adds to'the conductivity of theelcc' trolyte, but itdoes not alter the potential of thecopper conductors on the one hand, orthe silver conductors onthe other.

In short, the aspect of my invention just described con across a barrierseparating two pools of electrolyte in a potentiometric model byemploying a metal conductor acrossthe barrier from pool to pool, andintroducing ions of=the=same metal into the pools, and maintainingdifferent ionic activities in the two pools. T'heinvention contemplatesadjusting the potential dilterence between the pools by directadjustment of the ion concentration as well as by introducing into atleast one of the pools a substance which draws the ions into a weaklyionized complex. Moreover, the invention contemplates independentcontrol over both the potential across the barrier and the conductivityof the pools on either side by adding to. either or both pools anionizable salt that produces ions that are inert to the metal conductorand do not alter appreciably the activities of the metal ions.

These and other aspects of my invention will be understood morethoroughly in the light of the following detailed description, taken inconjunction with the accom panying drawing in which:

Fig. 1 is'a diagram, illustrating by means of a perspec tive view partlyin section, a potentiometric model of a well. penetrating two differentearth strata; and

Fig. 2.is a fragmentary section taken along the line 2-2. of Fig. 1' andshowing two electrolyte pools separated by a conductive barrier.

A1l.the phenomena which occur in a well bore are symmetrical withrespect to the axis of the well. Because of this symmetry, a well withits surrounding'formations can be represented by a wedge defined by twoplanes which contain the axis of the .well and cross each other on thataxis. Preferably the other wall of the wedge is a portion of a cylinderthe axis of which is that ofthe Well. The wedge may be the quadrant of acylinder having the well axis as its axis, or a smaller slice may beused, as shown in Fig. 1.

To facilitate the use of liquids in the model of Fig. 1,

its axis (the well axis it?) is disposed horizontally instead ofvertically, with the bottom 11 of its wedgeshaped tank 12 slopingdownwardaway from the axis. The liquid in the tank thus assumes awedge-shape, the bottom defining one face and the liquid level 13 theother. The tank has a curved Wall 14 on its deep side, the well axisbeing that of the curvature. This wall is fastened to the bottom and topie-shaped end walls 16, 17 which help to retain pools 19, 2t), 21 ofelectrolyte. A partition 22 running in the same direction as the wall 14and curved around the same axis separates a part of the slice near thewell axis from the rest of the slice. Thus the pool 19 near the axisrepresents the well bore, while the wider and deeper pools 20, 21represent respectively beds penetrated by the well. The bed pools areseparated from each other by a vertical pieshaped partition 23, which isparallel to the end walls. The liquid level in the Well bore pool 19 andthe bed pools is the same and rises to the well axis.

The walls and bottom of the tank are of insulating material. Thepartitions 22, 23 must have electrical properties appropriate to theproblem being studied. In other words, means must be provided forconducting electricity through or over these barriers at a plurality ofpoints along them, but the barriers should not be conductivelongitudinally. Fig. 2 illustrates suitable partition construction. Thusthe partition 23 is'irnpervious to liquid and keeps the two bed poolsseparate. It is composed of insulating plastic, but a multitude of finecopper wires 25 passes through the partition over substantially itsentire area, i. e. the rows of wires which make up the grid extendlongitudinally as well as vertically. The wires are insulated from eachother, so that effectively the partition is 'a conductor only in thedirection normal to its major surfaces. The partition 22 which separatesthe bed pools from the Well here pool is of similar construction.

The three electrolyte pools of the model have resistivitiescorresponding respectively to the bodies they represent, i. e. the twobeds and the mud in the well bore. A potential difference is maintainedthrough the partition 22 which separates the well bore pool from the bedpools and another potential diiference is maintained through thepartition 23 which separates the two bed pools. These potentialdifferences simulate those occurring at the boundaries in the wellrepresented by the partitions. The resistivities of the pools and thepotential differences through the barriers are established'in accordancewith the invention. Thus all three pools are aqueous solutionscontaining copper sulfate, the copper concentrations in the pools beingadjusted as already described to give the required potential difllerenceacross the barriers. the solutions thus prepared do not satisfy theresistivity requirements of the bodies they represent, resistivities areadjusted. Increase in resistivity of a pool is obtained by adding to apool a material, for example ammonia, in the case of copper, whichbindsthe copper ion into a Weakly ionized complex. Reduction in resistivityof a pool is obtained by adding a salt, say potassium chloride in thecase of copper, which increases conductivity without, within reasonablelimits, aifecting the activities of the copper ions.

If, in order to satisfy the requirements of the particular wellbeingstudied with the aid of the potentiometric model, it is necessary thatthe potentials of two barriers contacting the same electrolyte pool beindepedently variable, it is necessary to make the conductors associatedwith the two barriers of different metals. Take the case of the bed pool21 which is in contact with partition 23 and with part of the partition22. The latter two may be made independently variable by employingsilver wires in one and copper in the other, with the pool containingcopper sulfate and potassium chloride. Silver chloride will precipitateon the ends of the silver wires in contact with the pool and controlthe. potential dif ference through the barrier containing these wires.If necessary, the overall conductivity ofthe pool is adjusted by addingsodium nitrate, or some other ionizable salt which increasesconductivity Without affecting the activity of the copper or the silverconductors.

To simulate a self potential log with the model of Fig. 1, an exploringelectrode 30 is moved along the pool 19 (representing the mud or liquidin the well bore)., The exploring electrode is connected through arecording.

potentiometer 31 to a fixed electrode 32 disposed in the pool 20 at apoint corresponding to the earth surface. The potentials set up betweenthe two electrodes are measured at a plurality of points along the pool19 and plotted against the pool length, which represents depth in thewell bore. The length of the bed pools represent, of course, bedthicknesses. If desired, any

number of bed pools may be built into the model of Fig. 1, and separatedby partitions with current conductive means, resistivities in theindividual pools and potential differences across the partitions beingadjusted as already described.

The control of potential difference across a barrier through adjustmentof ion activity by the formation of complexes has been described withreference to copper and the copper-ammonium complex. There are numerousother examples. 7

With two pools of silver nitrate electrolyte separated by a barrierprovided with a silver conductor, potential across the barrier may bechanged by adding potassium cyanide to one of the pools, thus reducingsilver ion activity in that pool through the plex KAg(CN) The complexammonium chloro plumbate (NHQ PbCI is weakly ionized and its formationin an electrolyte pool will reduce lead ion activity in the pool andthus alter potential across the barrier separating that pool fromanother. The formation of lead silico fluoride in a pool of electrolytefrom a more highly ionized lead salt will have a similar effect.

The addition of sodium hexametaphosphate to a cadmium chlorideelectrolyte produces a complex and re duces cadmium ion activity. Apractical application of this complex in a potentiometric model havingmore than one barrier is as follows:

(1) Pool of aqueous cadmium chloride solution;

(2) Barrier provided with cadmium conductors;

(3) Pool of aqueous cadmium chloride solution to which sodiumhexametaphosphate is added;

(4) Barrier provided with gold conductors;

(5) Pool of aqueous cadmium chloride solution.

The invention may be practiced without relying upon electrolytic actionbetween the metal of the conductor and the same metal in ion form in theelectrolyte. In

other words, the conductor may be inert, in the sense:

that this term is usually employed in discussions of electrolytic cells,while the potential difference is developed by an electrolyticoxidation-reduction reaction within the pool. For example, the conductoracross the barrier may be platinum with potential development due to theconversion of ferric to ferrous ions, or of ferrous to ferric ions inthe pool. To consider a specific case, the first compartment of apotentiometric model may contain a pool of aqueous copper sulphatesolution. The second electrolyte pool contains copper sulphate in verysmall concentration and ferrous and ferric sulphates in greaterconcentrations. The barrier separating the first formation of the com-7. two. pools iscrossed by a copper conductor. The third electrolytepool contains potassiumchloride plusthallic and thallousnitrates and thebarrier which separates the second and third pools is crossed by aninert gold conductor. In themodel justdescribed, current flow is fromthe first to the: second and thence to the third pools under. theinfluence of self potentials developed between. the pools.Copperiontends to plate to copper on the conductor in the first pool andcopper from the conductor tends to go into solution and become ionizedin the second pool. However, ferrous ion tends to oxidize to ferric ion.at the. copper conductor in the first pool, thusinhibiting thesolutionof the copper while generating ferric ion, with resultantproduction of apotential acrossthe first barrier. At'the second barrier, whichseparates the second andthirdpoolsand is crossed by thegold-conductor,.ferric ion formedlin thesecond pool is reduced-to:ferrous ion, while intthe third pool thallous ion'is oxidized at thegold conductor to thallic ion, with result production of a potentialover the second barrier.

The potential to be developed across a barrier in any given instance maybe determined accurately from a table of standard oxidation-reductionpotentials. Consider a potentiometric model having' afirst'pool ofsilver nitrate and a second pool containing acidified stannousand-starmic chloride solutions,-th'e'two being separated by a barrierprovided with a silver conductor. Unit activities and a temperature-0525 C. are assumed.

The value of. thcoxidation-reduction potential in volts, referred to thehydrogen-hydrogen ion couple as zero for the reaction Sn++/Sn++++ is+0.l3. The co-rrc spending value for the Ag/Ag+ reaction is +0398, sothat the voltage difference across the barrier under theconditions-assumed is 0.798 rninus 0'.13 or 0.668v0lts.

Some silver will go into solution in the second pool but theconcentration is small, and may bederived as follows:

where E is the voltage across the barrier, i. e. 0.668'and Ag+isthe'molal concentration of silver required for equilibrium in thesecond bath.

Substitutingthe value of .668 in the equation anrl' solving for Ag+, itis found that this concentration is l0 In short, only. a veryl smallamount of silver will dissolve from the conductor into the: second bath,whereupon solution will cease but the potential diiferencc across thebarrier will continue to be maintained.

To take a second example, let the first pool contain cupric ion (Cu+{-)with titanous (Ti++) and titanic (Ti+++),ions in the second bath, theconductor through the barrier between baths being copper. Unitactivities and a temperature of 25 C. are again assumed, and under theseconditions the oxidation-reduction potential for Ti++/Ti+++ is .37 whilethat for Cu/Cu+-lis +344. The voltage across the barrier under theconditions assumed is the sum of .344 and .37 or .714. The equilibriumconcentration in mols of copper for the second pool is derived from 06log 1 2 011+ i. e.,

The application of the invention is not limited to potentiometric modelsof wells, but may be used in any potentiometric model in which it isdesired to establish a potential difference across abarrier separatingpools of electrolyte. Thus it can be used in potentiometric models ofoil or gas structures, dams, solid conductors of heat, and modelsrepresenting electrical discharge devices; condensers, insulators, etc.

I claim:

i. In a process for simultaing in a potentiometric model the conditionsexisting in a physical system in which a difference analogous to adifference in an electrical potential exists at a boundary between twoparts of the system, the improvement which comprises separating twoparts of themodel corresponding to the two parts of the system with anonconductive barrier corresponding in shape and location to theboundary, disposing pools of electrolyte corresponding respectively tothe two parts of the system in contact with the barrier on oppositesides of it, connecting the pools with a metallic conductor, andproducing potential difference between the two pools by galvanic actionincluding electrochemical equilibrium at each contact between metallicconductor and pool of electrolyte, the two pools both containing ionscorresponding to the metal of the conductor but in differentconcentrations so that the two pools and the metallic conductor act asaconcentration cell.

2. In a process for simulating in a potcntionietric model the conditionsexisting in a physical system in which a difference analogous to adifference in an electrical potential exists at a boundary between twoparts of the system, the improvement which comprises separating twoparts of the model corresponding to the two parts of the system with anonconductive barrier corresponding in shape and location to theboundary, disposing pools of electrolyte corresponding respectively tothe two parts of the system in contact with the barrier on oppositesides of it, connecting the pools with a metallic con ductor, andproducing potential difference between the two pools by galvanic actionincluding electrochemical equilibrium at each contact between metallicconductor and pool of electrolyte, the two pools both containing ionscorresponding to the metal of the conductor and a substance beingintroduced into at least one of the pools which forms a weakly ionizedcomplex of the ions of the metal, thereby producing a differentconcentration of the ions or the metal in the two pools and causing thetwo pools and the metal conductor to act as a concentration cell andproduce the potential difference between the pools.

3. In a process for simulating in a potentiometric model the conditionsexisting in a physical system in which a difference analogous to adifference in an electrical potential exists at a boundary between twoparts of the system, the improvement which comprises separating twoparts of the model corresponding to the two parts of the system with anonconductive barrier corresponding in shape and location to theboundary, disposing pools of electrolyte corresponding respectively tothe two parts of the system in contact with the barrier on oppositesides of it, connecting the pools with a metallic conductor, andproducing potential difference between the two pools by galvanic actionincluding electrochemical equilibrium at each contact between metallicconductor and pool of electrolyte, bothpools containing ionscorresponding to the metal of the conductor but in differentconcentrations so that the two pools and the metallic conductor act as aconcentration cell and produce the potential difference between thepools, the conductivity of at least one of the pools: being changed byintroducing into it an ionizable salt that produces ions that are inertto the metal conductor and do not alter appreciably the electrochemicalactivity of the ions of the metal.

4. In a process for simulating in a potentiometric model the conditionsexisting in a physical system in which a difference analogous to adifference in an electrical potential exists at a boundary between twoparts of the system, the improvement which comprises separating twoparts of the model corresponding to the two parts of the system with anonconductive barrier corresponding in shape and location to theboundary, disposing pools of electrolyte corresponding respectively tothe two parts of tl e system in contact with the barrier on oppositesides of it, con

'76 necting the pools with a metallic conductor, introducing 9 ions intoone of the pools of electrolyte to make the composition of that pooldifferent from the composition of the other pool, and to produce at thecontact between that pool and the metallic conductor a voltage differentfrom that existing at the contact between the conductor of the otherpool, thereby producing potential difference between the two pools bygalvanic action including electrochemical equilibrium at each contactbetween metallic conductor and pool of electrolyte, and introducing ionsof a different kind into one of the pools to change the conductivity ofthe pool without affecting appreciably the activity of the ions whichproduce the potential difference between the pools.

5. In a process for simulating in a potentiometric model the conditionsexisting in a physical system in which a difference analogous to adifference in an electrical potential exists at a boundary between twoparts of the system, the improvement which comprises separating twoparts of the model corresponding to the two parts of the system with anonconductive barrier corresponding in shape and location to theboundary, disposing pools of electrolyte corresponding respectively tothe two parts of the system in contact with the barrier on oppositesides of it, connecting the pools with metallic conductor means with theindividual metallic conductors which interconnect pools being composedof the same metal throughout the length of the conductor, andintroducing ions into one of the pools of electrolyte to make thecomposition of that pool of electrolyte different from the compositionof the other pool of electrolyte and producing at the contact betweenthe pool to which the ions are introduced and the metallic conductor avoltage. different from that existing at the contact between themetallic conductor and the other pool of electrolyte, thereby producingpotential difference between the two pools by galvanic action includingelectrochemical equilibrium at' each contact between metallic conductorand pool of electrolyte.

6. In a process for simulating in a potentiometric model the conditionsexisting in a physical system in which a difierence analogous to adifference in an electrical potential exists at a boundary between twoparts of .the system, the improvement which comprises separating twoparts of the model corresponding to the two parts of the system with anonconductive barrier corresponding in shape and location to theboundary, disposing pools of electrolyte corresponding respectively tothe two parts of the system in contact with the barrier on oppositesides of it, con- '10 necting the pools with a metallic conductor, andintroducing ions into one of the pools of electrolyte to make thecomposition of that pool of electrolyte different from the compositionof the other pool of electrolyte and producing at the contact betweenthe pool to which the ions are introduced and the metallic conductor avoltage different from that existing at the contact between the metallicconductor and the other pool of electrolyte, thereby producing potentialdifference between the two pools by galvanic action includingelectrochemical equilibrium at each contact between metallic conductorand pool of electrolyte.

7. In a process for simulating in a potentiometric model the conditionsexisting in a physical system in which a difference analogous to adifference in an electrical potential exists at a boundary between twoparts of the system,

the improvement which comprises separating two parts of the modelcorresponding to the two :parts of the system with a nonconductivebarrier corresponding in shape and location to the boundary, disposingpools of electrolyte corresponding respectively to the two parts of thesystem in contact with the barrier on opposite sides-of it, connectingthe pools with a metallic conductor, introducing ions into one of thepools of electrolyte to make the composition of that pool of electrolytedifferent from the composition of the other pool of electrolyte andcarrying out an oxidation-reduction reaction in at least one of thepools so that the two pools and the metallic conductor act as anelectrochemical oxidation-reduction cell and produce at the contactbetween the pool to which the ions are introduced and the conductor avoltage different I from that existing at the contact between theconductor and the other pool, thereby producing potential ditferencebetween the two pools by galvanic action including electrochemicalequilibrium at each contact between metallic conductor and pool ofelectrolyte.

' Electrochemistry by Creightion, vol. 1,. 4th edition (1943), pp. 166,199-201, 227. r

Bersworth Chem. Co., Versene" Tech BulL No. 1,

Jan. 14, 1949, p. 10.

